the geometry of cosmology using none toembed none in asp.net web,windows application QR Code Symbol Versions n the last two none for none chapters we have made a lot of progress in exploring the future and past of the Universe, basically just by using local Newtonian gravity. We argued that the dynamics of an expanding, homogeneous and isotropic cosmology can be calculated from Newtonian gravity, at least if the pressure in the Universe is negligible, because all we need to look at is the local Universe, the part nearest us. The assumption that the Universe is homogeneous guarantees that the rest of the Universe will behave the same as our local region.

But this line of reasoning has its limitations. Even if we calculate the dynamics of the Universe this way, we don t learn what the distant parts of the Universe will look like in our telescopes. The curvature of space, which is not part of a Newtonian discussion, will affect the paths of photons as they move through the Universe.

Moreover, if we want to ask deeper questions about the Universe, such as those we pose in the next chapter, then we should know something more about its the larger-scale structure. For this, we must turn to full general relativity. Only general relativity can provide a consistent picture over the vast scales we shall need to explore, out to where the cosmological speed of recession approaches the speed of light.

So it is now time to learn about Einstein s description of cosmology.. In this chapte r: we explore the three different geometries that a homogeneous and isotropic cosmology can assume. We see how to construct two-dimensional versions of these, which shows us why there are only three possibilities. We see how astronomical observations can measure this geometry directly.

As we have seen, Einstein s theory has the simplifying property that only matter within our past light-cone matter that can send signals to us can have in uenced the evolution of the Universe we observe. This is logically much more satisfying than Newtonian gravity, where matter everywhere affects us with its gravity instantly. In fact, scientists did not study cosmology seriously before Einstein: the logical dif culty of applying Newtonian gravity to an in nite Universe, coupled with the fact that astronomers before the twentieth century had no idea how large the Universe was, left scientists with little to work with.

When Einstein s theory showed how to treat gravity in a causal way and provided consistent cosmological models, scientists began to explore the subject. The basically Newtonian view of cosmology we developed in the last two chapters was still based on relativity: we had to use the two facts that (1) only matter in our past light-cone affects our gravitational eld, and (2) general relativity allows us to ignore the gravity due to spherical mass distributions further away from us than the galaxy whose motion we are computing. For homogeneous universe models, we were then able to ignore most of relativity and study the dynamics with essentially Newtonian equations.

We will develop below the relativistic counterparts of these model universes, and we will see that in many situations they are remarkably similar. But relativity is richer than Newtonian gravity. There are model universes that are not describable in Newtonian terms.

Here is an example. Imagine a homogeneous universe in which the expansion is different in different directions. For example, imagine that the Universe were expanding at twice the rate.

In this sectio none for none n: the large-scale shape of the Universe could be very complex. Even if the Universe is homogeneous, it could be anisotropic: different in different directions..